We report an analytical and numerical investigation into the impact of helicity inversion in LHC processes that do not conserve lepton number $(L)$. As a case study, we focus on the production and decay of Majorana neutrinos $(N)$ through on- and off-shell $W$ bosons in the Phenomenological Type I Seesaw model. Using the Monte Carlo event generator \texttt{MadGraph5\_aMC@NLO} in conjunction with the \texttt{HeavyN} model libraries, we perform exact matrix element (ME) computations without the narrow width approximation. Despite helicity inversion appearing explicitly in MEs, we report the absence of helicity suppression of $L$-violating collider observables for $1\to4$ and $2\to4$ processes that are dominated by resonant $N$ production. We attribute this incongruity to the different scalings of 4-momenta and squared 4-momenta in MEs and squared MEs, with exact cancelations occurring in the latter when $N$ goes on-shell in the small-width limit. In off-shell regimes, total suppression / enhancement of $L$ violation can emerge. Implications for other neutrino mass models are discussed.
The helicity of a Dirac neutrino with mass $m$ evolves under the influence of a $B$-field because it has a magnetic dipole moment proportional to $m$. Moreover, it was recently shown that a polarized or anisotropic medium engenders the same effect for both Dirac and Majorana neutrinos. Because a $B$-field polarizes a background medium, it instigates helicity oscillations even for Majorana neutrinos unless the medium is symmetric between matter and antimatter. Motivated by these observations, we review the impact of a $B$-field and of an anisotropic or polarized medium on helicity oscillations …
We introduce the Majorana spinors in the momentum representation. They obey the Dirac-like equation with eight components, which has been first introduced by Markov. Thus, the Fock space for corresponding quantum fields is doubled (as shown by Ziino). The particular attention has been paid to the questions of chirality and helicity (two concepts which frequently are confused in the literature) for Dirac and Majorana states.
Usually it is supposed that Majorana neutrino produced in the superposition state $χ_L = ν_L + (ν_L)^c$ and then follows the neutrinoless double beta decay. But since weak interactions are chiral invariant then the neutrino at production has definite helicity (i.e., $ν_L$ and $(ν_L)^c$ neutrinos are separately produced and then neutrino is not in the superposition state). This helicity cannot change after production without any external interactions. Thus we see that for unsuitable helicity the neutrinoless double $β$ decay is not possible even if neutrino is a Majorana particle. Also transiti…
Massive neutrinos can have helicity $s_{\parallel}\neq -1$. Neutrino helicity changes when the neutrino interacts with an external magnetic field and it is possible that the left-handed neutrinos born inside the Sun or a supernova could leave their sources with a different helicity. Since Dirac and Majorana neutrinos have different cross sections in the scattering on electrons for different neutrino helicities, a change in the final neutrino helicity may generate a different number of events and spectra in terrestrial detectors when astrophysical neutrinos have travelled regions with strong ma…
We perform a comprehensive and model-independent analysis for characterizing the spin and dynamical structure of the production of a non-diagonal pair of Majorana particles with different masses and arbitrary spins, $e^-e^+\to X_2 X_1$, followed by a sequential two-body decay, $X_2\to Z X_1$, of the heavier particle $X_2$ into a $Z$ gauge boson and the lighter particle $X_1$ escaping undetected at high-energy $e^+e^-$ colliders. Standard leptonic $Z$-boson decays, $Z\to \ell^-\ell^+$ with $\ell=e$ or $μ$, are employed for precisely diagnosing the $Z$ polarization influenced by the production a…
Author proposes the idea of direct, affordable in the foreseeable future experiment that could determine whether the neutrino are Dirac or Majorana particles.
For Majorana dark matter, gauge boson bremsstrahlung plays an important role in enhancing an otherwise helicity-suppressed s-wave annihilation cross-section. This is well known for processes involving a radiated photon or gluon together with a Standard Model fermion-antifermion pair, and the case of massive electroweak gauge bosons has also recently been studied. Here we show that internal Higgs bremsstrahlung also lifts helicity suppression and could be the dominant contribution to the annihilation rate in the late Universe for dark matter masses below ~1 TeV. Using a toy model of leptophilic…
We construct self/anti-self charge conjugate (Majorana-like) states for the (1/2,0)+(0,1/2) representation of the Lorentz group, and their analogs for higher spins within the quantum field theory. The problem of the basis rotations and that of the selection of phases in the Dirac-like and Majorana-like field operators are considered. The discrete symmetries properties (P, C, T) are studied. Particular attention has been paid to the question of (anti)commutation of the Charge conjugation operator and the Parity in the helicity basis. Dynamical equations have also been presented. In the (1/2,0)+…
A general and comprehensive analysis for the vector currents of two massive particles, $X_2$ and $X_1$, with arbitrary integer-spin values is given. Our special focus is on the case when two particles are charge self-conjugate, i.e. Majorana bosons. The general structure of their couplings to an on-shell or off-shell vector boson $V$ is described in a manifestly covariant way and then the constraints on the triple vertex due to discrete CP symmetry and the Majorana condition of two particles being Majorana are worked out. The validity of our full analytic investigation is checked by studying t…
Cosmic background neutrinos ($C_νB)$ helicity composition is different for Dirac or Majorana neutrinos making detectors based on $C_νB$ capture sensitive to the nature of neutrinos. We calculate, for the first time, the helicity changes of neutrinos crossing dark matter fields, to quantitatively calculate this effect on the capture rate. We show that a fraction of neutrinos change their helicity, regardless of them being deflected by a void or a dark matter halo. The average signal from the 100 most massive voids or halos in a Gpc$^3$ gives a prediction that if neutrinos are Dirac, the density…
Neutrinos propagating in media (matter and electromagnetic fields) undergo flavor and helicity oscillations, where helicity transitions are instigated both by electromagnetic fields and matter currents. In addition, it has been shown that correlations between neutrinos and antineutrinos of opposite momentum can build up in anisotropic media. We re-derive the neutrino equations of motion in the mean-field approximation for homogeneous yet anisotropic media, confirming previous results except for a small correction in the Majorana case. Furthermore, we derive the mean-field Hamiltonian induced b…
We analyze both chirality-changing and chirality-preserving transitions of Dirac-Majorana neutrinos. In vacuum, the first ones are suppressed with respect to the others due to helicity conservation and the interactions with a (``normal'') medium practically does not affect the expressions of the probabilities for these transitions, even if the amplitudes of oscillations slightly change. For usual situations involving relativistic neutrinos we find no resonant enhancement for all flavour-conserving transitions. However, for very light neutrinos propagating in superdense media, the pattern of os…
Neutrino flavor conversion studies based on astrophysical environments usually implement neutrino mixings, neutrino interactions with matter and neutrino self-interactions. In anisotropic media, the most general mean-field treatment includes neutrino mass contributions as well, that introduce a coupling between neutrinos and antineutrinos termed helicity or spin coherence. We discuss resonance conditions for helicity coherence for Dirac and Majorana neutrinos. We explore the role of these mean-field contributions on flavor evolution in the context of a binary neutron star merger remnant. We fi…
We study the possibilities to detect Majorana neutrinos in $e^- γ$ colliders for different center of mass energies. We study the $W^- W^- l_j^{+}(l_j^+\equiv e^+ ,μ^+ ,τ^+)$ final state which are, due to leptonic number violation, a clear signature for intermediate Majorana neutrino contribution. Such a signal (final lepton have the opposite charge of the initial lepton) is not possible if the heavy neutrinos are Dirac particles. In our calculation we use the helicity formalism to obtain analytic expressions for the amplitude and we have considered that the intermediate neutrinos can be either…
The problem if existing neutrinos are Dirac or Majorana particles is considered in a very pedagogical way. After a few historical remarks we recall the theoretical description of neutral spin 1/2 particles, emphasizing the difference between chirality and helicity which is important in our discussion. Next we describe the properties of neutrinos in the cases when their interactions are given by the standard model and by its extensions (massive neutrinos, right-handed currents, electromagnetic neutrino interaction, interaction with scalar particles). Various processes where the different nature…
We present a new technique for the calculation of helicity $\pm 1/2$ gravitino production during preheating. It is based on the equivalence between goldstinos and helicity $\pm 1/2$ gravitinos at high energies. The problem is thus reduced to the standard (Majorana) fermion production after inflation. Comparison with the results obtained in the unitary gauge is also presented.
The lepton number violating signal of like-sign-dileptons (LSD), p p \to \ell^\pm\ell^\pm + 2 jets, is investigated within a model of mixing in the neutrino sector assuming the existence of heavy Majorana neutrino states with a left--handed coupling to the light leptons. The LSD signal receives contributions both from the resonant production of a heavy Majorana neutrino (N) and from the exchange of a virtual N in the WW fusion mechanisms. These two possibilities are discussed in detail and compared. Helicity amplitudes are given pointing out differences with calculations previously reported by…
A rather elusive helicity reversal occurs in a gedanken experiment in which a massive left-handed Dirac neutrino, traveling at a velocity u < c, is overtaken on a highway by a speeding vehicle (traveling at velocity v with u < v < c). Namely, after passing the neutrino, looking back, one would see a right-handed neutrino (which has never been observed in nature). The Lorentz-invariant mass of the right-handed neutrino is still the same as before the passing. The gedanken experiment thus implies the existence of right-handed, light neutrinos, which are not completely sterile. Furthermore, overt…
We study the possibility of dark matter in the form of heavy neutrinos from a fourth lepton family with helicity suppressed couplings such that dark matter is produced thermally via annihilations in the early Universe. We present all possible constraints for this scenario coming from LHC and collider physics, underground direct detectors, neutrino telescopes, and indirect astrophysical searches. Although we embed the WIMP candidate within a model of composite dynamics, the majority of our results are model independent and applicable to all models where heavy neutrinos with suppressed couplings…
We review our results on the calculation of helicity 1/2 gravitino production during preheating. The method we present is based on the equivalence between goldstinos and longitudinal gravitinos at high energies. The problem is thus reduced to the standard (Majorana) fermion production after inflation. Comparison between helicity 3/2 and 1/2 production and with the results obtained in the unitary gauge is also presented.
The production of heavy sterile neutrinos from $π^-,K^-$ decay at rest yields charged leptons with negative helicity (positive for $π^+,K^+$). We obtain the branching ratio for this process and argue that a Stern-Gerlach filter leads to spatially separated domains of both helicity components with abundances determined by the branching ratio. Complemented with a search of monochromatic peaks, this setup can yield both the mass and mixing angles for sterile neutrinos with masses in the range $3 MeV \lesssim m_s \lesssim 414 MeV$ in next generation high intensity experiments. We also study oscill…
If massive neutrinos possess magnetic moments, a magnetic field can cause a spin flip. In the case of Dirac neutrinos the spin flip converts an active neutrino into a sterile one and vice versa. By contrast, if neutrinos are Majorana particles, a spin flip converts them to a neutrino of a different flavor. We examine the behavior of neutrinos in a random magnetic field as it occurs, for instance, in certain astronomical objects, such as an active galactic nucleus. Both Dirac and Majorana neutrinos behave ergodically: independently of their initial density matrix, they tend towards an equiparti…
In this paper, We find that the angular distribution of two-body decay and scattering process that can be studied by introducing the helicity method.It has been argued that the angular distribution only depends on magnitude of the decaying amplitude which final particle momentum is along the $Z$ axis. Therefore, when calculating the angular distribution,we only need to know the helicity amplitude in the $Z$ direction. At the same time, we also discuss the symmetry of physical processes, such as parity and time inversion transformation and so on. The effects of these symmetric transformations o…
The production of Like-Sign-Di-leptons (LSD), in the high energy lepton number violating ($ΔL = +2$) reaction, p p --> 2jets + l+l+ (l=e,μ,τ) of interest for the experiments to be performed at the forthcoming Large Hadron Collider (LHC), is investigated in detail, taking up a composite model scenario in which the exchanged virtual composite neutrino is assumed to be a Majorana particle that couples to the light leptons via the $SU(2)\times U(1)$ gauge bosons through a magnetic type coupling ($σ_{μν}$). An helicity projection method is used to evaluate exactly the tree-level amplitudes of the c…
We propose neutrino mass spectroscopy using Er$^{3+}$:Cs$_2$NaYF$_6$ or :Y$_2$O$_3$ crystal placed in hollow of a Bragg fiber as a target system. Unknown neutrino parameters and properties such as the lightest neutrino mass, Majorana/Dirac distinction, and CP violating phases can be explored by measuring scattered photons ($γ$) along the excitation (and fiber) axis by varying Raman trigger ($γ_0$) directions, in Er$^{3+}$ de-excitation process from $|e\rangle $ state to $|g\rangle $ state; $|e\rangle \,, | e\rangle + γ_0 \rightarrow | g\rangle + γ+ ν_i\barν_j$, $ν_i\,, i = 1, 2,3$ being a mass…
Relic neutrinos from the Big Bang decoupled from the hot plasma predominantly in helicity eigenstates. Their subsequent propagation through gravitational inhomogeneities of the Universe alters the helicities of both Dirac and Majorana neutrinos, thus providing an independent probe of the evolving universe. We determine here the probability that relic neutrinos flip their helicity, in terms of the spectrum of density inhomogeneities measured in the Cosmic Microwave Background. As we find, for Dirac neutrinos the gravitational helicity modifications are intermediate between the effects of magnet…
Massive neutrinos demand to ask whether they are Dirac or Majorana particles. Majorana neutrinos are an irrefutable proof of physics beyond the Standard Model. Neutrinoless double electron capture is not a process but a virtual $ΔL=2$ mixing between a parent $^AZ$ atom and a daughter $^A(Z-2)$ excited atom with two electron holes. As a mixing between two neutral atoms and the observable signal in terms of emitted two-hole X-rays, the strategy, experimental signature and background are different from neutrinoless double beta decay. The mixing is resonantly enhanced for almost degeneracy and, un…
Massive neutrinos demand to ask whether they are Dirac or Majorana particles. Majorana neutrinos are an irrefutable proof of physics beyond the Standard Model. Neutrinoless double electron capture is not a process but a virtual $ΔL = 2$ mixing between a parent $^AZ$ atom and a daughter $^A(Z-2)$ excited atom with two electron holes. As a mixing between two neutral atoms and the observable signal in terms of emitted two-hole X-rays, the strategy, experimental signature and background are different from neutrinoless double beta decay. The mixing is resonantly enhanced for almost degeneracy and, …
In three generations or more, we derive the oscillation probabilities of both Dirac and Majorana neutrinos relativistically by using the Dirac equation. We present various oscillation probabilities for including wrong-helicity neutrinos, right-handed neutrinos, and anti-neutrinos. We summarize the relations between these probabilities. As neutrinos have finite mass, there are two components for each chirality corresponding to positive and negative helicities. We show that the probability is different for each component even if neutrinos have the same chirality. The probabilities derived by the…
We present, how a systematic study of $B \to D\ell N$ ($D \to K \ell N$) decays with $\ell=μ,τ$, at Belle II (BESIII) can provide unambiguous signature of a heavy neutrino $N$ and/or constrain its mixing with active neutrinos $ν_\ell$, which is parameterized by $|U_{\ell N}|^2$. Our constraint on $|U_{μN}|^2$ that can be achieved from the full Belle II data is comparable with what can be obtained from the much larger data set of the upgraded LHCb. Additionally, our method offers better constraint on $|U_{μN}|^2$ for mass of sterile neutrino $m_N < 2$ GeV. We can also probe the Dirac and Majora…
The local supercluster acts as a gravity deflection source for cosmic background neutrinos. This deflection by gravity changes the neutrino helicity and therefore has important consequences for ground based tritium capture experiments aimed at determining if the neutrino is Dirac or Majorana. Here we explore the deflection effect of the local supercluster using the higher resolution DEMNUni simulation suite and reaffirm our previous results. We show that the lightest neutrinos are ultra-relativistic enough to suffer little deflection by gravity and at the same time not relativistic enough to a…
We compute the nucleosynthesis bounds on the masses of stable Dirac and Majorana neutrinos by solving an evolution equation network comprising of all neutrino species which in the Dirac case includes different helicity states as separate species. We will not commit ourselves to any particular value of the nucleosynthesis bound on effective number of light neutrino degrees of freedom $N_ν$, but present all our mass bounds as {\em functions} of $\dNu$. For example, we find that the excluded region in the mass of a Majorana $μ$- or $τ$- neutrino, $0.31$ MeV $< m_ν^M < 52$ MeV corresponding to a b…
